You are required by the NY State Vehicle and Traffic Law to file an accident report if you are involved in any accident where there is damage to the property of one individual (including yourself) that is more than $1,000. The report must be filed within 10 days.
DMV keeps accident reports for only 4 years from the date of the accident, except for rare instances that are described in Vehicle and Traffic Law Section 201(i). You can search and order reports online.